Many advanced control techniques are formulated as optimization problems, which can be solved by programming. One class of such techniques is optimization-based receding time horizon control, such as model predictive control (MPC). There are MPC formulations for both linear and nonlinear systems. Nonlinear MPC solves nonlinear programs in real-time, which can be a challenging task due to limited computing resources, the complexity of the problem to solve, or the time available to solve the problem. Therefore, most of the practical applications are based on a linearity assumption or approximation. The linear MPC typically solves a quadratic programming problem.
The MPC is based on an iterative, finite time horizon optimization of a model of a system and has the ability to anticipate future events to take appropriate control actions. This is achieved by optimizing the operation of the system over a future finite time-horizon subject to constraints, and only implementing the control over the current timeslot. For example, the constraints can represent physical limitations of the system, legitimate and safety limitations on the operation of the system, and performance limitations on a trajectory. A control strategy for the system is admissible when the motion generated by the system for such a control strategy satisfies all the constraints. For example, at time t the current state of the system is sampled and an admissible control strategy minimizing the cost is determined for a relatively short time horizon. Specifically, a real-time calculation determines a cost-minimizing control strategy until time t+T. Only the first step of the control strategy is implemented, then the state is sampled again and the calculations are repeated starting from the current state, yielding a new control and new predicted state path. The prediction horizon keeps being shifted forward and for this reason MPC is also called receding horizon control.
The MPC can be used to generate the actual trajectory of the motion of the system based on the model of the system and the desired reference trajectory by solving an optimal control problem over a finite future time horizon subject to various physical and specification constraints of the system. The MPC aims for minimizing performance indices of the system motion, such as the error between the reference and the actual motion of the system, the system energy consumption, and the induced system vibration.
When compared to other control strategies, the MPC has the advantage of explicitly accounting for constraints and the ability to handle multiple inputs and outputs. However, the MPC is computationally expensive because it requires that an optimization problem be solved at each time step in order to calculate the control output of the system.
An explicit MPC (EMPC) is formulated as a way of dealing with these limitations. In the explicit MPC the optimization part of the problem is solved offline, prior to implementing the controller. The solution to the offline part of the algorithm is represented as a set of adjacent, convex regions in an n-dimensional state space. The real-time part of the control process searches the state space to determine which region the system is currently operating in. Each region is associated with a set of coefficients used to calculate the control output, see, e.g., WO2013/136090.
The EMPC reduces the amount of real-time computation required to implement an MPC controller by shifting part of the computation offline. However, the real-time part of the EMPC may still require many thousands operations for searching the state space, which makes explicit model predictive controllers implemented using general purpose computing units and circuitry too slow for some real-time control applications, especially when the MPC optimal control problem has many decision variables and/or constraints.
Application-specific circuits are customized for a particular use, rather than intended for a general-purpose use. In contrast with the general purpose circuitry, it is always a challenge to optimize the design of the application-specific circuits for the specific problem. Accordingly, there is a need to provide the application-specific circuit for controlling a system using the EMPC.